Ito process as numerical solution of stochastic differential equation

The 2nd example/test is based on a stochastic SIR model, with parameter vector \theta=(a,b,c,d), the SDE is characterized by

f_{\text{drift}}(x) = (-ax_1x_2 + d, ax_1x_2 -(c+d)x_2, cx_2-dx_3)^t
f_{\text{diffusion}}(x) = (-bx_1x_2 , bx_1x_2, 0)^t

numerical results from ito_process_euler below show Ito processes that range from stable to unstable.